People Are Bad At Math

I've refrained from posting things pertaining to my (unfortunate) persuit of a math degree for some time, because frankly, to the extent I ever feel a mathematical inclination, I use it to add three or four words to my spiralling-out-of-control-in-length thesis. Maybe when I'm in classes again next semester, and not just writing this god forsaken thing, I'll get back into the swing of making long, obtuse posts about utility calculations.

In the mean time, here's a short, obtuse post about utility calculations!

Last night, I was watching a new gameshow that's called "Deal, or No Deal." The basic premise of the show is that there are 28 numbered suitcases. One suitcase has $1,000,000, one has $750,000 all the way down in various incriments to a $1 and $.01. The contestant gets to choose one, and a bunch of attractive women stand with the rest. The contestant chooses five suitcases to open, each one of which has its value inside, eliminating (obviously) the possibility that their own chosen case contains that amount. After five iterations, Howie Mandell (of Bobby's World), the host of this monstrosity, gets a call from an ethereal "banker," who is hidden behind some glass up in a booth, who presents an "offer" based on the revealed values - typically, these offers start fairly low (in the $9,000 range) and go up as the lower amounts are eliminated, and varies based on the probability-weighted value of the suitcase the person has. This goes on through a few iterations (choose one suitcase, offer, choose three suitcases, offer, and so on) until the person either has eliminated every case but their own, or they take the deal.

(By the way: Howie Mandell, what the fuck. He has a shaved head and a soul patch, and looks, for all the world, like Lore from the old Brunching Shuttlecocks site. It's scary - I didn't even recognize him until, mocking one of the contestants' mothers, he made a voice that sounded eerily familiar, until I realized he was doing Bobby from Bobby's World)

After an hour of watching the show, however, it's obvious that the contestant should almost never take the deal. In one case, there were six values on the board ($10.000, $500.000, $400.000, $300.000, $100, $750). In this instance you have an expected payout of roughly $200,000 (actually a touch higher, but not that much) - yet the offer that came from the booth was $99,000. The guy then eliminated $100 and $10.000, and was left with an expected payout of around $300,000, and the offer was $240,000.

At this point, it should be noted, the $60.000 risk premium might be worthwhile, but from a pure risk/reward standpoint, he should obviously continue on. So, the next case he picked was $400.000, meaning an expected payout of $264.000 - and the offer that comes down is $140.000 - and he immediately accepts.

In any case, this got me thinking about a general model of the game - theoretically, playing the game such that you take the case and never consider the deal, the payout adjusted for risk is $114.000. I can't decide if this means that your inclinations during the course of the game are sufficiently disruptive to your rationality (I mean, the show is also designed to fuck with you and be suspenseful) that the correct action is to work your way up to an offer above that, and accept, barring extraordinary circumstances (ie: you eliminate all but the high-values prior to the offer reaching that level.) Who knows. What I took away from the show is that women are bad at math.

The only other interesting thing was, they allow you to bring four guests with you. The guy in the above example brought his mother, fiance, and a couple people whose relation was less obvious (my personal belief is that the guy doesn't know anyone else, but they wanted him to look more popular.) At the point where there was a $240,000 offer down, even though it is theoretically not in your interest to do so, his fiancee suggested he accept.

At that point, Jamison's third law is: you do what she says. The potential to gain $60,000 is not worth the loss of her appropriating your manhood.